Problem: Simplify the following expression: $t = \dfrac{a^2 - 4a - 5}{a - 5} $
First factor the polynomial in the numerator. $ a^2 - 4a - 5 = (a - 5)(a + 1) $ So we can rewrite the expression as: $t = \dfrac{(a - 5)(a + 1)}{a - 5} $ We can divide the numerator and denominator by $(a - 5)$ on condition that $a \neq 5$ Therefore $t = a + 1; a \neq 5$